Analyzing the Structure of Binary Test Responses Using an Optimal Scaling Approach.
James S. Roberts, Karen M. Samuelsen · 2002
This study explored alternative methods of estimating the number of latent dimensions represented by binary test data. The alternative methods vary in their complexity and include: (1) the minimum average partial correlation technique (MAP; W. Velicer, 1976) applied to phi correlations between binary responses; (2) the bootstrapped parallel analysis method (A. Buja and N. Eyuboglu, 1992) applied to phi correlations; (3) the minimum average partial correlation technique applied to data that has been optimally scaled using a monotonic transformation in which tied data may be untied (J. Kruskal, 1964; SAS Institute, 1999); (4) the bootstrapped parallel analysis procedure applied to those same optimally scaled responses; and (5) the DETECT procedure (J. Zhang and W. Stout, 1999). The binary responses were simulated with either a one-dimensional or a two-dimensional three-parameter logistic model, and then those responses were analyzed with each of the five dimensionality estimation techniques. The mean difference between the estimated and true dimensionality suggested that the MAP and DETECT procedures performed best, on average, in conditions where the data were truly unidimensional. In contrast, the bootstrapped parallel analysis and theDETECT procedures performed best, on average, in the two-dimensional data conditions. In addition, the bootstrapped parallel analysis estimated were less sensitive to the amount of correlation between latent dimensions relative to those produced by the DETECT procedure. These limited simulations suggest that the bootstrapped parallel analysis procedure may be useful to applied researchers and students who have little access to or knowledge of technically sophisticated dimensionality assessment. (Contains 4 figures and 27 references.) (Author/SLD) Reproductions supplied by EDRS are the best that can be made from the original document. Analyzing the Structure of Binary Test Responses Using an Optimal Scaling Approach JaMes S. Roberts Karen Samuelsen University of Maryland Paper presented at the annual meeting of the National Council on Measurement in Education, New Orleans, Louisiana PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS BEEN GRANTED BY